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Discrete Mathematics 1

Your first course in DM and mathematical literacy: logic, sets, proofs, functions, relations, and intro to combinatorics

4.9 ★★★★★1,000 studentsCreated by Hania Uscka-WehlouLast updated Nov 16, 2025🌐 English

What you'll learn

✓How to solve problems in chosen Discrete-Mathematics topics (illustrated with 395 solved problems) and why these methods work, step by step.

✓Elementary Logic, including proving tautologies that involve implications, conjunctions, and disjunctions; necessary and sufficient conditions.

✓Elementary Set Theory, including working with intersections and unions of sets, and other set-related topics.

✓An introduction to mathematical theories, with concepts like axiom, theorem, primitive notion, etc.

✓The concept of function between two discrete sets: injections, surjections, bijections.

✓The concept of (a binary) relation as a subset of Cartesian product of two sets: RST relations, order relations, etc.

✓RST relations and the concept of equivalence classes; an illustration for a modulo relation between integers.

✓Functions as relations; various ways of depicting functions between two discrete sets; equipotent sets.

✓An introduction to the topic of sequences, only basic concepts that can be needed in Combinatorics; we come back to the topic of sequences in DM3.

✓Various proof techniques, including direct proofs, proofs by contradiction, proofs by contrapositive, Mathematical Induction, and Pigeonhole Principle.

✓A preparation for Combinatorics: the concept of index, the sigma sign (with computational rules), n factorial, n choose k, Pascal's Triangle, Binomial Theorem.

✓A brief introduction to Combinatorics: the art of counting. Permutations, combinations, paths, etc; the topic will be continued in the first sections of DM2.

✓Playful logical problems and riddles, including the famous Zebra Puzzle (Einstein's Riddle), and some classical riddles about liars and truth tellers.

✓This is the first course in Discrete Mathematics, so don't worry that neither Number Theory nor Graph Theory are covered; they will be covered in a sequel.

Requirements

•Basic high school mathematics (mainly arithmetic)

•You are always welcome with your questions. If something in the lectures is unclear, please, ask. It is best to use QA, so that all the other students can see my additional explanations about the unclear topics. Remember: you are never alone with your doubts, and it is to everybody's advantage if you ask your questions on the forum.